Operating Cycle 1: Brief Description

Here is a quick description of the ADR cycle. We'll go over it in more detail
after the temperature-entropy diagram.

Rapid Cooldown

The magnetic field is dropped rapidly. The salt pill cools as the
molecular magnetic moments drop out of alignment with the field, absorbing
entropy.

Slow Cooling

Once the cooling reaches the desired temperature, the rapid decrease of
the magnetic field stops. Heat slowly leaks in from outside. The magnetic
field is slowly dropped, to allow the salt pill to absorb the heat without
increasing in temperature.

Warmup

When the salt pill has absorbed all the heat it can, the magnetic field
is increased again. The salt pill warms as the magnetic moments align and dump
their energy.

Dumping Heat

When the salt pill is hotter than the thermal sink, the heat switch is
turned on. Heat flows from the salt pill into the thermal sink. Then the heat
switch is turned off and the cycle begins again.

Operating Cycle 2: Temperature Entropy Diagram

I have a fairly long description of the following graph for those who'd like
a guided tour. I wrote it originally for users with text browsers, then
realized that its slightly different approach might be useful to anyone with
any type browser. Feel free to read my graph
description, or to read this page, or to try both.

This diagram shows how the temperature and entropy of the salt pill vary through
the cycle. The vertical axis of the graph is entropy divided by the universal
gas constant, R, and is therefore unitless. The horizontal axis is temperature
in degrees Kelvin (that is, absolute temperature.)

The green curve near the bottom shows the entropy of the pill at high field. The
blue curve higher in the graph shows entropy at zero field. At any temperature,
the zero-field entropy is higher than the high field entropy. The zero-field
entropy includes both the entropy of random thermal motion (heat energy) as well
as the entropy of the disordered magnetic moments. The high field entropy
includes only the thermal randomness, since the magnetic moments are all lined up
by the field.

The lines between the two curves show ADR cycles, an "ideal" cycle, which is
shown as a rectangle, and a "non-ideal" cycle, which extends along a curved line
to higher temperatures and which overlaps the full-field curve for some distance.
The stages of the ideal cycle are labelled 1 through 4 on the graph. Here are
descriptions of those stages:

1. Rapid Cooldown

Entropy: Constant

Temperature: Dropping Fast

Heat Switch: Off

Magnetic Field: Dropping Fast

As operators turn down the magnetic field, the magnetic moments disalign. As
they disalign, they convert entropy of random thermal vibrations into entropy of
random alignments of the magnetic moments. That is, as the moments absorb heat
energy and thus cool the salt pill. Because the cooldown is rapid (only a few
minutes in the XRS ADR), there is not time for a significant amount of heat to
flow into the salt pill. Thus, the entropy of the pill is essentially contstant
as the temperature drops.

2. Slow Cooling

Entropy: Increasing Slowly

Temperature: Constant

Heat Switch: Off

Magnetic Field: Dropping Slowly

Once the salt pill reaches operating temperature, operators stop
the rapid drop of the magnetic field. If they then held the field constant, the
salt pill would gradually warm over a period of several hours as heat slowly
leaked in from the surroundings. Instead, the operators slowly drop the magnetic
field, allowing the molecular magnetic moments to slowly absorb the heat energy
that leaks in. In the XRS ADR, this constant temperature, slow cooling phase
lasts several hours. (The rapid cooldown only lasts a few minutes.)

3. Warmup

Entropy: Constant

Temperature: Increasing Rapidly

Heat Switch: Off

Magnetic Field: Increasing Rapidly

When the magnetic field reaches zero, operators must dump the
stored heat. They first increase the magnetic field (rapidly, so as not to waste
time.) As the field increases, the molecular magnetic moments fall into
alignment with the field. The entropy they stored as randomness of alignment
becomes entropy of random thermal motion. That is, as the magnetic moments
align, they heat the salt pill by dumping energy into it.

4. Dumping Heat

Entropy: Decreasing

Temperature: Constant

Heat Switch: On

Magnetic Field: Constant, High

When the salt pill becomes warmer than the heat sink, operators
turn on the heat switch. Heat now flows from the salt pill to the heat sink.
(In the XRS ADR, the heat sink is a bath of liquid helium at 1.3 K.) As heat
flows from the salt pill, its entropy drops. After dumping heat, the operators
turn off the heat switch and start the cycle again.